Manuscript VIII-A@3 · VIII-A-v3.tex · section · 2398a747

Recovery distinctions used only as interface safeguards

Recovery distinctions used only as interface safeguards · lines 2554–2567

These finite-dimensional statements are included to make the non-identification beside Option N self-contained. They do not extend the geometric model.

For states and channels, use

d_{tr} (ρ, σ) = \frac{1}{2} ∥ ρ - σ ∥_{1}, d_{⋄} (Φ, Ψ) = \frac{1}{2} ∥ Φ - Ψ ∥_{⋄} .

The diamond norm is the stabilized trace norm; all channel comparisons include arbitrary untouched references.

Displayed formulas in this passage

unlabeled · line 2561
$d_{tr} (ρ, σ) = \frac{1}{2} ∥ ρ - σ ∥_{1}, d_{⋄} (Φ, Ψ) = \frac{1}{2} ∥ Φ - Ψ ∥_{⋄} .$